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How many zeros are the end of ?

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vomhorizon
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How many zeros are the end of ? [#permalink] New post   15 Nov 2012, 07:23
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00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

74% (01:15) correct 26% (01:22) wrong based on 1809 sessions
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How many zeros are at the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95

Show Spoiler
In order to find the number of zeros we have to find out the number of 5's and 2's , because no. of 5's will be less then the number of 2's ..
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C
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Bunuel
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How many zeros are the end of ? [#permalink] New post   15 Nov 2012, 07:41
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vomhorizon wrote:
How many zeros are the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95


380! has \(\frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}=76+15+3=94\) trailing zeros ( take only the quotient into account).

Answer: C.

For more on trailing zeros check: everything-about-factorials-on-the-gmat-85592.html

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Re: How many zeros are the end of ? [#permalink] New post   10 Sep 2017, 05:25
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380/5 = 76

76/5= 15

15/5= 3

Sum of these quotients. Answer C
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Re: How many zeros are the end of ? [#permalink] New post   13 Jan 2018, 15:57
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rnz wrote:
Bunuel wrote:
vomhorizon wrote:
How many zeros are the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95


380! has \(\frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}=76+15+3=94\) trailing zeros ( take only the quotient into account).

Answer: C.

For more on trailing zeros check: https://gmatclub.com/forum/everything-ab ... 85592.html
Similar questions to practice:
https://gmatclub.com/forum/if-60-is-writ ... 01752.html
https://gmatclub.com/forum/how-many-zero ... 00599.html
https://gmatclub.com/forum/find-the-numb ... 08249.html
https://gmatclub.com/forum/find-the-numb ... 08248.html
https://gmatclub.com/forum/if-n-is-the-p ... 01187.html
https://gmatclub.com/forum/if-m-is-the-p ... 08971.html
https://gmatclub.com/forum/if-p-is-a-nat ... 08251.html
https://gmatclub.com/forum/if-10-2-5-2-i ... 06060.html
https://gmatclub.com/forum/p-and-q-are-i ... 09038.html
https://gmatclub.com/forum/question-abou ... 08086.html
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https://gmatclub.com/forum/what-is-the-g ... 05746.html
https://gmatclub.com/forum/if-d-is-a-pos ... 26692.html
https://gmatclub.com/forum/if-10-2-5-2-i ... 06060.html

Hope it helps.


How do you know how many times you need to add the fractions?


This is explained in highlighted post.
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Re: How many zeros are the end of ? [#permalink] New post   13 Jan 2018, 15:47
Bunuel wrote:
vomhorizon wrote:
How many zeros are the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95


380! has \(\frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}=76+15+3=94\) trailing zeros ( take only the quotient into account).

Answer: C.

For more on trailing zeros check: https://gmatclub.com/forum/everything-ab ... 85592.html

Similar questions to practice:
https://gmatclub.com/forum/if-60-is-writ ... 01752.html
https://gmatclub.com/forum/how-many-zero ... 00599.html
https://gmatclub.com/forum/find-the-numb ... 08249.html
https://gmatclub.com/forum/find-the-numb ... 08248.html
https://gmatclub.com/forum/if-n-is-the-p ... 01187.html
https://gmatclub.com/forum/if-m-is-the-p ... 08971.html
https://gmatclub.com/forum/if-p-is-a-nat ... 08251.html
https://gmatclub.com/forum/if-10-2-5-2-i ... 06060.html
https://gmatclub.com/forum/p-and-q-are-i ... 09038.html
https://gmatclub.com/forum/question-abou ... 08086.html
https://gmatclub.com/forum/if-n-is-the-p ... 06289.html
https://gmatclub.com/forum/what-is-the-g ... 05746.html
https://gmatclub.com/forum/if-d-is-a-pos ... 26692.html
https://gmatclub.com/forum/if-10-2-5-2-i ... 06060.html

Hope it helps.


How do you know how many times you need to add the fractions?
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Re: How many zeros are the end of ? [#permalink] New post   14 Jan 2018, 09:25
vomhorizon wrote:
How many zeros are at the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95

Show Spoiler
In order to find the number of zeros we have to find out the number of 5's and 2's , because no. of 5's will be less then the number of 2's ..


\(\frac{380}{5} = 76\)
\(\frac{76}{5} = 15\)
\(\frac{15}{5} = 3\)

So, the total number of 0's in the end of 380! is 76+15+ 3 = 94 , answer will be (C)
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Re: How many zeros are the end of ? [#permalink] New post   08 Jan 2020, 22:38
Bunuel wrote:
vomhorizon wrote:
How many zeros are the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95


380! has \(\frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}=76+15+3=94\) trailing zeros ( take only the quotient into account).

Answer: C.

Hope it helps.



Is there any good tip to have the result of the division (380/5^2=15) in an easier way?

Thanks for any response.
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Re: How many zeros are the end of ? [#permalink] New post   06 Jan 2021, 12:46
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vomhorizon wrote:
How many zeros are at the end of 380! ?

(A) 90
(B) 91
(C) 94
(D) None
(E) 95

Show Spoiler
In order to find the number of zeros we have to find out the number of 5's and 2's , because no. of 5's will be less then the number of 2's ..


The basic formula for that is: \(\frac{380}{5}+\frac{380}{5^2}+\frac{380}{5^3}; 5^4 \)is larger than 380.

\(=76+15+3=94\)

The answer is C.

Another way, considering the basic formula:
380/5=76
76/5=15
15/5=3

76+15+3=94
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Re: How many zeros are the end of ? [#permalink] New post   06 Jan 2021, 13:30
\(\frac{380}{5}+\frac{380}{25}+\frac{380}{125}\)
=76+15+3 (not considering the remainders)
=94
Answer: C
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Re: How many zeros are the end of ? [#permalink] New post   18 Oct 2023, 05:33
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